## Jonathan D.H. Smith

*A class of quasigroups solving a problem of ergodic theory *

Comment.Math.Univ.Carolinae 41,2 (2000) 409-414. **Abstract:**A pointed quasigroup is said to be semicentral if it is principally isotopic to a group via a permutation on one side and a group automorphism on the other. Convex combinations of permutation matrices given by the one-sided multiplications in a semicentral quasigroup then yield doubly stochastic transition matrices of finite Markov chains in which the entropic behaviour at any time is independent of the initial state.

**Keywords:** quasigroup, Latin square, Markov chain, doubly stochastic matrix, ergodic, superergodic, dripping faucet, group isotope, central quasigroup, semicentral quasigroup, $T$-quasigroup, left linear quasigroup

**AMS Subject Classification:** 20N05, 60J10

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